In a high pressure compressor comprising an annular casing having installed therein a plurality of stages of bladed rotor wheels, it is known that the first rotor wheel is particularly sensitive in terms of operability. It is known to take air under pressure from one of the stages of the compressor itself and to reinject it upstream from the first rotor wheel, and in the vicinity thereof. Conventionally, air is reinjected through holes or tubes that pass through the outer shroud of the casing. The air flow is guided to be as tangential as possible relative to the wall of the casing.